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ROSE TREE MEDIA SCHOOL DISTRICT

COURSE CURRICULUM

COURSE TITLE: AP Physics C – Mechanics, Level IGRADE LEVEL:

CREATION DATE: July 2002

AP Physics C – Mechanics, Level I of 52 July 2002

MISSION STATEMENT

1. First and foremost, this IS a college level course and is taught at THAT level. The course is designed to prepare students for the AP Physics C Exam in Mechanics. Students who have already attended college have returned to critique this course for its appropriateness and level of difficulty. Five universities, in particular, help determine the level of difficulty, because these are some of the most challenging that OUR students have attended: MIT, CAL Tech, RPI, Stanford, and Carnegie Mellon.

2. Lab work is all self-designed and original ideas must be applied to set problems. The AP Physics C Exam has designated about 17% of the scoring will test students’ knowledge of data-gathering, graphical, statistical analysis, and qualitative/quantitative assessments of what this data means.

3. Much of the strategy in the instruction revolves around “spiraling concepts.” An idea or technique such as derivatives, integrals, vectors, definitions, formulas, etc are introduced in one unit, then they are reintroduced again and again in later chapters. Students are specifically shown that this is a familiar topic, used again in a new application. Hopefully, it will help them build upon what they have already learned and reinforce how important it is to thoroughly understand the concept the FIRST TIME around.

4. Much emphasis is put on using calculus with their other math skills. Although some class time is used to show how these equations are derived, the emphasis on how they are used to solve problems. Most students take calculus concurrently with physics and will see this derivation process there. Students, who do not take calculus concurrently, will always have access to an appendix that lists these formulas for their use.

5. AP Physics students form the core leadership role for Physics Olympics and the building events for Science Olympiad. They select the team captains, even leaders, times after school, alternates, and competition groups. They are responsible for running elimination contests to decide which building projects will represent our school at the tournaments. They rate these devices and grade them. They take attendance at all practices and tournaments and are generally responsible for running ALL aspects of the competition teams, including tracking costs. This kind of responsibility is important in developing leadership skills.


Essential Question, Concept or Theme: A. Calculus Introduction Approx. Time Allotment: 1 weekPA Standards: 3.1.12 A,B,C,D,E

Benchmark/Skills Assessment Aligned Materials/Resources/Technology Instructional Strategies

A.Benchmark # 1 Demonstrate proficiency in basic math skills needed to do all algebraic problem solving and graphing throughout the year.

Benchmark #2 Appropriately use derivatives to differentiate an equation in order to graph this function, or solve for a specific answer.

Benchmark # 3 Appropriately use integrals to integrate an equation, in order to graph this function, or solve for a specific answer.

A. 1. Two quizzes, testing these two basic skills.2. One homework assignment of 20 problems is given to check students’ knowledge of these two skills.

A.1. Textbook (Math Appendices)2. Teacher generated worksheets3. Graphing calculator

A.1. Remedial help sessions are offered mornings and afternoons the week before school begins.2. Remedial help is offered after school until 5:00 p.m., after 5:00 p.m. by appointment, during ”C” lunch, and after 8:00 p.m. by telephone.3. Classroom help sessions are structured: students may work individually or in groups, at desks and lab tables in the back of the room … one-on-one or specific problems are handled by the teacher at the front of the room, and announced so that individuals can come “forward” when needed.



Adaptations/Inclusion Techniques Enrichment Strategies Remediation Strategies Multicultural/Interdisciplinary

ConnectionAll Units A – J can be adapted to any individual IEP.

. Students with physical handicaps have full access to academic classroom exercises, as well as laboratory exercise. We have handicapped accessible desks. We also rotate student lab groups, which will also change their contribution to the group during each lab exercise.

. Students with mental handicaps can have individual IEP’s developed so that they can compete to the best of their ability with all comparably capable students.

All units A – J.What opportunities can be offered students OUTSIDE the regular classroom, to enhance and enlarge their experience. How can we give them applicable credit for this effort?

1. Extra Credit. Each student may receive no more than 50 EXTRA CREDIT POINTS each marking period, They may receive points for:a. Correctly answering designated questions in class.b. Catching the teacher making mistakes (especially spelling and problem solutions).c. Each student is required to do four building projects (one each marking period). Exceptionally well-done devices, or students or who help evaluate other students’ devices, can receive such points.d. Making insightful comments, or demonstrating “extended thinking.”e. Participating in Physics Olympics or Science Olympiad competitions.f. Students who, after school, help, find, pickup, or help distribute materials for other students’ use.2. Students who demonstrate real capability in lab exercises can become lab assistants, who help set up and run labs for their classmates.3. While students are generally permitted to select their own seating placement in class – teachers may assign seats as needed . . . do well and you may freely select your seat.4. Teachers select lab group

All units A – J require a high level of mathematical competency. This is addressed before the course begins.

1. A week before school begins, tutoring and review sessions are offered each day to assess and help their capabilities.

2. Once school begins, teachers are available for extra help during the day, when free; immediately after school; by mutual appointment; when the after-school activity period ends, i.e. 5:20 p.m.; in the evening and weekends with telephone support.

3. Students, who fail ANY assignment, lab report or test/quiz, may correct ALL mistakes and resubmit it. If properly done, it is recorded as a 60%, a passing grade.

4. Homework assignments are optional for students.

5. Each chapter unit is usually three to four weeks in length. Tests are on the last Friday of each unit. If class periods present themselves for a chapter review before the test, they are used as such. Our present lab/classrooms provide an excellent opportunity to divide classes for this activity. Students who wish to work in groups, may work together at the lab tables; students who wish to work alone, may pull individual desks to the back of the room; students who wish one-on-one or small group interaction directly with the

All units A-J.WORD PROBLEMS . . . they are part of every math course . . . they are singular to Physics.

An interdisciplinary connection with the Math Department is crucial. This is a mutually reinforcing combination. IF YOU CAN LEARN MATH . . . CAN YOU USE IT!?!?

The laboratory exercise and report are basic to ALL SCIENCE. They require the qualitative and quantitative analysis of what students discover in experimentation. CAN THEY DESCRIBE AND COMMUNICATE WHAT THEY EXPERIMENTALLY FIND?!?! The expository form of writing is a needed discipline which the Language Arts and Science Departments should mutually support.

The Art and Science Departments have cooperated to research, design, draw, document, and build balsa wood bridges. They then BREAK them to see how successful they were. Successful students can compete in the Illinois Institute of Technology's annual International Bridge Building Tournament.

The Physical Education teachers and athletic coaches at Penncrest have the Science Department's motion detectors evaluate athlete's motion from rest. Mass, force, acceleration, momentum and impulse can all be measured.




Connectioncombinations. Individual talents can be distributed through the class, so that overlapping or conflicts can be avoided . . . Even more, students with leadership, organization, data gathering, mathematical, computer or hands-on building skills can, and should, be grouped with other students, who appreciate and can augment their skills. This is an important consideration . . . because later we do not choose the people in life we work with . . . we just learn how to work with them!5. Students who excel in and out of class may request a letter of recommendation for their college applications. These letters are carefully written and document these contributions and personal developments.

teacher, come forward to the front desk.

6. Starting in April, teachers are available for evening sessions to prepare for the AP Physics C – Mechanics Exam, college placement, and military entrance exams.

7. Teachers make a very determined effort to help students who need it. Students, who make an active choice to miss class for another commitment, bear the responsibility to make up the work themselves.

An interdisciplinary connection needs to exist between the Administration and Science Departments to facilitate laboratory exercises. ALL double lab periods occur on Tuesdays and Wednesdays, for ALL upperclassmen, for ALL WEEK. If these sessions can be avoided for class assemblies; workshop days; mentoring sessions; and unique scheduling, like IEP's. This is a significant development.

Also, the first remediation session runs the week before school begins, it overlaps with beginning school activities. Physics teachers will run remediation sessions that DO NOT conflict with "opening school activities." Physics teachers, who have this opening schedule, when they mail students in beginning August, can exempt these times for students and parents.

The most significant interdisciplinary connect that that does exist with Physics, is the Technology Department. Physics students' building projects are planned, drawn, reproduced, diagrammed and built with their help. This department has constantly worked with us to develop and build student projects, using software, hardware, and draftsmanship quality drawings. They are one reason for our overall success in building competitions.


Essential Question, Concept or Theme: B. One Dimensional Motion Approx. Time Allotment:PA Standards: 3.1.12 A,C,D,E; 3.2.12 A,B,C,D; 3.4.12 C; 3.6.12 B; 3.7.12 A,B,C,D,E


B.Benchmark # 1 Describe and evaluate the motion of an object undergoing ANY kind of motion in a straight line.a. Define displacement, velocity, acceleration, surge, and alpha, beta (etc., terms of motion.b. Drive the universal equation for displacement in one dimension.c. Graph these quantities vs. time, and find these values at any position or time.d. Differentiate and integrate known graphs in order to produce related graphs of the same motion.e. Plot graphs of any straight line motion with given data, and differentiate and integrate these graphs using Vernier Graphical Analysis III software.f. Identify and define vector and scalor quantities related to motion.g. Derive algebraically the five kinematic equations for an object undergoing constant acceleration.h. Use these kinematic equations to solve single object motion, multiple motions by one object or related motions of two objects (man trying to catch a bus).i. Derive, using calculus, all related equations of motion, for an object undergoing inconstant acceleration.j. Use calculus to solve for specific values of motion, deriving from the universal displacement equation for one dimension.

Benchmark # 2 Evaluate the motion of an object undergoing inconstant acceleration, in an original laboratory exercise of their design.a. Predict the motion of this object

B.1. Two graphing quizzes.2. One multiple-choice quiz on chapter concepts.3. One chapter test with a multiple-choice section. To be done in class. The test also has seven problems, and students must select two of the seven to be done and turned in as homework.4. One major homework assignment of selected problems from the end of the chapter, to be turned in with the take-home test.5. One laboratory exercise: The object undergoing inconstant acceleration.6. An optional building project or leadership role in either Physics Olympics or Science Olympiad.

B.1. Graphing calculator2. IBM PC computer3. PASCO 750 Interface Box4. PASCO Photogates5. PASCO Smart Pulleys6. PASCO Accelerometers7. PASCO Software8. Vernier Graphical Analysis III Software9. Microsoft Excel10. Microsoft Word

B.1. Students will construct in the lab a device, which undergoes inconstant acceleration. They will predict what this motion will look like graphically, by producing qualitative graphs of displacement, velocity, acceleration, and surge vs. time. This will form the basis of their hypothesis, and define what they are measuring. Finally, tin their conclusion, they will compare their predictions to the actual graphs they obtained by doing the lab. They will also address major sources of error.2. Students will have three weeks to write and do the lab: 1st lab session – decide what you will do and write a formal procedure for teacher approval.2nd lab session – After approval, run the lab. 3rd lab session – adjustments or re-run any trials with questionable data. Upon completion, one week and a formal lab write-up (word-processed only!) is handed in.3. The major concepts being “spiraled” in this unit are:a. Graphing techniquesb. Using derivatives and anti-derivatives to produce other related graphsc. Addressing and deriving formulas as concept statements (what is the formula telling you, as to its motion).d. Using calculus to manipulate formulase. Problem-solving techniques.f. Using a graphing calculator for problem solving.4. Students will begin the selection of


Essential Question, Concept or Theme: B. One Dimensional Motion Approx. Time Allotment:PA Standards: 3.1.12 A,C,D,E; 3.2.12 A,B,C,D; 3.4.12 C; 3.6.12 B; 3.7.12 A,B,C,D,E


graphically … before experimenting.b. Qualitatively and quantitatively describe the motion and relate it to the actual graphs obtained during the experiment.c. Describe all sources of error, which affect the overall results.

Physics Olympics team captains and event leaders for the fall tournament. These individuals will begin choosing an overall team and dividing them into events. They will define their responsibilities for each event, such as attendance, how much credit per person, a calendar of activities, deadlines, selection processes, and how to divide these responsibilities among themselves. Also, they will choose an overall team administrator and a web-site manager. 5. Students will begin recruiting and assigning building events to students wishing to participate in Science Olympiad, whose competition events begin in mid-March. Dividing these responsibilities and awarding credit will be their decision, based on how much effort is made by students each marking period.


Essential Question, Concept or Theme: B. One Dimension Motion Approx. Time Allotment: PA Standards: 3.1.12 A,C,D,E; 3.2.12 A,B,C,D; 3.4.12 C; 3.6.12 B; 3.7.12 A,B,C,D,E


ConnectionSee Unit A See Unit A See Unit A See Unit A


Essential Question, Concept or Theme: C. Vectors Approx. Time Allotment: 2 weeksPA Standards: 3.1.12 A,B,C,D,E; 3.2.12 B,D; 3.4.12 C; 3.7.12 A,B,D


C.Benchmark # 1 Diagram vectors in two dimensions using mathematical or directional axes.a. Define vectors and contrast them to scalar values.

Benchmark # 2 Diagram vectors in three dimensions.a. Draw and evaluate vectors in an I-j-k component format.b. Draw and evaluate vectors in a resultant format.c. Convert one format to the other, depending upon which one is given at the start.

Benchmark # 3 Add and subtract vector quantities in two and three dimenisons.a. Draw vectors graphically, and add and subtract them using the head-tail method to find the resultant.b. Draw vectors mathematically from a common origin, and resolve each into components.c. Add and subtract components, and resolve their total into a single resultant value.

Benchmark # 4 Multiply and divide vector quantities in two and three dimensions.a. Define a vector dot product, and relate it to scalar values.b. Derive the dot product formula in component or resultant format.c. Use the dot product formula to solve problems in the resultant or component format.

C.1. Quiz – multiple choice on chapter concepts.2. Quiz – three problems.3. Test – same format as the chapter test in part B.4. Homework – selected problems from the end of the chapter.5. Laboratory Exercise – Equilibrium in Three Dimensions.6. Participation in Physics Olympics or Science Olympiad.7. Class participation for points.

C.1. Graphing calculator2. IBM PC3. PASCO 750 Interface Box4. PASCO smart pulleys5. Vernier Graphical Analysis III6. Microsoft Excel software7. Microsoft Word software8. Spring scales9. Standard single pulleys10. Tabletop hardware

C.1. Vectors is one of the most important topics to “spiral” through the year – it will be used in every unit from here on.a. Use the lab to introduce equilibrium in three dimensions. First have them measure displacement vectors and calculate their components. Use these values to find the forces and their components, by using proportions. Reinforce – “it is the same system for any vector value (displacements, forces, velocities, etc.).”b. The velocity concept mentioned above will be used to introduce the next chapter, “Velocities in Two and Three Dimensions.”c. Briefly introduce dot and cross products defined as Work and Torque. They had these last year and will be able to relate the system (vector products) to the scalar value (work), and the vector value (torque). L These will be addressed in later chapters as major topics.2. Relate three dimensional vector calculations to matrices. Use the graphical calculators to calculate components in two and three dimensions. Demonstrate why uniform methods of drawing vectors is essential to calculations, since the formulas are derived from these standard formats.3. Show them the three methods for calculating cross products in the I-j-k format: a) formula, b) diagram, c) relational. Each method will “do the job,” so let students utilize the method which works best for them and makes the most




d. Define a vector cross product formula in component or resultant format.f. Use the cross product formula to solve problems in the resultant or component format.

Benchmark # 5 Qualitatively relate dot and cross products to known values.a. Define Work as a dot product.b. Define torque as a cross product.

sense to them.4. Start them early preparing for Physics Olympics and Science Olympiad. This is their first time in an independent leadership role, and they need much guidance in how to do it successfully. Also, they need to understand the support role that the teacher plays in this relationship for materials, information, rules and finances.5. The instructor also needs to do a strong critique of their first lab. Hopefully it can be read and evaluated by more than one person and hopefully by someone at the college level. MUCH emphasis is put on the laboratory exercises this year, because the College Board has dictated that one-third of the free-form problem solving portion of the AP Physics C Exam, be dedicated to “laboratory situations and applications.”


Essential Question, Concept or Theme: D. Motion in Two and Three Dimensions Approx. Time Allotment: 4 weeksPA Standards: 3.1.12 A,B,C,D,E; 3.2.12 B,C,D; 3.4.12 C; 3.6.12 C; 3.7.12 A,B,C,D,E


D.Benchmark # 1 Evaluate an object’s motion in two or three dimensions.a. Define and calculate total displacement of an object in two or three dimensions, in the component or resultant format.b. Define and calculate the total velocity of an object in two or three dimensions, in the component or resultant format.c. Define and calculate the total acceleration of an object in two or three dimensions, in the component or resultant format.d. Use differential calculus to derive velocity, acceleration, surge, etc., from the universal displacement equation, written in the I-j-k format. This equation is displacement, with respect to time. e. Use vector addition to combine I-j-k components to find resultant displacements, velocities, accelerations, etc., at any position or time.f. Sketch, identify and analyze graphs of motion for displacement, velocity, acceleration, surge, etc., for motion in the i, j, or k direction.

Benchmark # 2 Evaluate an object’s motion as a projectile on earth (or under other gravitational constants).a. Define a projectile’s constant horizontal motion due to inertia, and derive equations of motion with respect to time.b. Define a projectile’s accelerated vertical motion due to gravity, and derive equations of motion with respect to time.c. Combine components of horizontal and

D.1. Quiz – multiple choice on chapter concepts.2. Two quizzes – each three problems on “multiple motion.”3. Test – same format as the chapter test in part B.4. Homework – selected problems from the end of the chapter.5. Laboratory Exercise –I. Find the algorithm for a PASCO Launcher to predict actual ranges.II. Hit the target, with a ball rolling down a ramp.6. Participation in Physics Olympics or Science Olympiad7. Class participation for points.

D.1. If spiraling topics works – use the ideas of kinematics and vectors to have students define and explain and derive multiple motion and its equations. Have them differentiate how this is done in a component format, (first), then how it is combined into a resultant format. This methodology should be utilized with the reading of the chapter units, so that students can develop these ideas intuitively, or with the aid of the reading material. Either way, make them work for it in the classroom, then put it in their notes, in their own words.2. Note taking has been emphasized throughout the year to date, but now it takes on a new significance – students are combining multiple concepts, and levels of thought. Come chapter test time, or more importantly, final exam and AP exam time ... which is easier to review? ... the entire textbook, or your concise notes, written in your own words? Stress note taking.3. The laboratory exercises are very different. The first is to find an algorithm to add or multiply with the predicted range of a launcher, so that the combination will identify the actual range the PASCO launcher throws a marble. This is done for every 5o of elevation of the launcher. Students must utilize the Microsoft Excel and Vernier Graphical Analysis III software to really do this lab. It really stretches their ability to utilize these packages to do the bulk of the calculations, come up with a list of %




vertical motion with vector addition to find the resultant displacement, velocity, acceleration of the projectile at any position or time.

Benchmark # 3 Evaluate an object’s motion, as it moves uniformly, in a circular path.a. Define the object’s constant speed and changing velocity, then derive equations for each one.b. Derive the equation for centripetal acceleration using components of the change in velocity with vector addition. Then do the same thing using the resultant values of velocity in a circle.c. Calculate an object’s speed, velocity, displacement, and centripetal acceleration for any position or time.

Benchmark # 4 Evaluate two objects’ motion, relative to one another, in one and two dimensions.a. Define relative motion for two objects, in terms of “frames of reference.”b. Drive equations for this motion, in one and two dimensions, as seen from either “frame of reference.”c. Solve problems for any kinematic value, including time for either object, as it moves relative to the other.

errors for each 5o of elevation, find how they differ every 5o, and then find an overall algorithm to reduce all the errors simultaneously. There is no one way to do this, and we have seen five or six different approaches to the problem over the years. The second lab is one session … walk into the room … be given the problem: to hit a target with an adjustable ramp (elevation) with an adjustable length, that a ball must roll along. The target is scored like an archery ring target, and they may use any method to predict the effects of two simultaneous variables: elevation and length. They are then given five trial positions by the teacher, and must place the target on the floor to hit center, without a test roll. It is fast-paced, open thinking, with some luck and too many ideas to try in one period. You just love this one.


Essential Question, Concept or Theme: E. Forces and Motion Approx. Time Allotment:PA Standards: 3.1.12 A-E; 3.2.12 B-D; 3.4.12 A, C; 3.6.12 C; 3.7.12 A-E


E. Benchmark # 1 Define and evaluate force as the “push” or “pull” on an object.a. Relate mass to the size of the object.b. Define mass as gravitational or inertial, and derive its’ units.c. Qualitatively, and then quantitatively, relate force and mass to acceleration.d. Derive units of force from mass and acceleration.e. Discriminate between mass and weight.f. Draw Free-Body-Diagrams (F-B-D) for any object, at rest or undergoing any kind of motion.g. Define “net force” and derive its’ equation.h. Calculate the net force on any individual object or system using vector resolution.

Benchmark # 2 Define and evaluate Newton’s First Law of Motion.a. Differentiate, both qualitatively and quantitatively, what is unique about his first law, compared to the other two, in terms of motion.b. Relate all three laws to one another in terms of force.c. Use F-B-D’s to define equilibrium.d. Use F-B-D’s to derive equations of equilibrium in resultant and component formats.e. Define inertia, and derive its’ unit of measurement.f. Differentiate inertia from a force, and relate it to F-B-D’s for any object in motion.g. Solve problems for unknown forces and

1. Quizzes-two will be given on multiple choice on chapter concepts.2. Quiz with three problems.3. Test-same format as the chapter test in part B4. Homework-selected problems from the end of the chapter.5. Laboratory exercise-coefficient of friction to Net Force Lab.6. Participation in Physics Olympics or Science Olympiad.7. Class participation for points.

1. Graphing calculator2. IBM PC3. PASCO 750 Interface Box4. PASCO Smart Pulleys & Photogates5. PASCO Picket Fences6. PASCO Force Meters and Accelerometers7. Vernier Graphical Analysis III Software8. Microsoft Excel & Word Software9. Spring scales10. Slotted weights and weight hangers11. Scales12. Tabletop hardware

1. The greatest single problem that a physics teacher faces, when he or she tries to explain some phenomenon is MISCONCEPTIONS! You, as the teacher, believe the student understands your explanation . . . but if they do not . . . this misconception is carried over into the next unit, . . . and the next . . . It is “spiraling” in reverse. You perpetuate the problem. This unit is especially difficult for students, because it encompasses a great many concepts, definitions, relationships, and derived thoughts. The teacher must CONSTANTLY question, and requestion students; give them examples that they must explain; encourage them to ask their own questions; and emphasize the multiple choice quiz and test preparation AND follow-up, to find and eliminate these misconceptions.2. This unit is two chapters in the textbook. It is easier to combine, than separate them. The first chapter is Force and Motion-I (Without Friction); the second chapter is Force and Motion-II (With Friction). Teach them everything . . .with friction . . . and be able to solve any kind of problem. The discriminator is them . . . “sometimes friction is so small it may be neglected from the overall solution, but it is always there in real life.”3. The number one misconception is that static friction: FFSTATIC = (MS) (FN)This is not always the case. This is how large static friction can be. Static friction is a reaction force, and if the action force




kinematic values, (including time), using equilibrium and Newton’s First Law of Motion

Benchmark # 3 Define and evaluate Newton’s Second Law of Motion.a. Relate the “unbalanced force” in his first law to net force, outside force, and resultant force, and show they are all the same.b. Differentiate “outside” forces from “internal” forces, using the concept of “system of forces.”c. Relate net force to acceleration.d. Derive the equation for the second law in component, and then resultant formats.e. Relate ALL kinematic motion to resultant force.f. Solve problems for any unresolved force or kinematic motion designated.

Benchmark # 4 Define and evaluate Newton’s Third Law of Motion.a. Define and identify Action-Reaction (A-R) pairs from examples given to students.b. Define “forces at a distance,” and identify their A-R pairs, especially gravity.c. Explain friction as a reaction force.d. Solve problems for systems of internal and external forces.

Benchmark # 5 Evaluate friction as a force.a. Define and derive the two properties that create and affect the size of friction.b. Qualitatively and quantitatively describe and derive the equation for “normal force.”

is less than this value, the static friction will equal the action force. However, FFKINETIC = (MK) (FN) will always be true as the object slides along. 4. The topics needed to be “spiraled” in this unit, (for use in the next two units), will be a. Force and the calculation of its’ components.b. Using acceleration to relate and unite forces with motion. This is because acceleration is the ONLY variable found in both the kinematic AND force equations.c. There is no such thing as “centrifugal force,” this is actually inertia; and inertia is not a force. There is, however, centripetal force. This is a net force, and creates a unique system called “dynamic equilibrium.” This concept is absolutely essential when you start the double chapter unit on Rotational Motion and Rolling. d. Units, Units, Units5. It is usually about this time the Physics Olympics has its’ first tournament in the autumn. If need be, use lab periods to permit the AP Physics kids to organize their events, make announcements, draw up schedules, and mostly communicate with each other, since it is the only time that they can be together to get this done. These are usually the students who are MOST involved in after school activities. It is usually easier for them to come in after school to do labs in groups of four or five, than to get together as the single Physics Olympics Leadership.




c. Qualitatively and quantitatively describe and derive the equation for the coefficient of static and kinetic friction.d. Derive the equation for the force of friction.e. Define and derive the equations for “drag force” and “terminal velocity.”f. Describe circular motion in terms of net force.g. Derive the equation for centripetal force, using the equation for net force.h. Solve problems for unknown values of friction, normal force, coefficients of friction, drag forces, and centripetal forces.



Adaptations/Inclusion Techniques Enrichment Strategies Remediation Strategies Multicultural/InterdisciplinaryConnection

See Unit A See Unit A See Unit A See Unit A


Essential Question, Concept or Theme: F. Work/Energy/Power Approx. Time Allotment:PA Standards: 3.1.12 A-E; 3.2.12 A-D; 3.4.12 A-D; 3.6.12 C; 3.7.12 A-E


F. Benchmark # 1 Define and evaluate kinetic energy. a. Derive equation for kinetic energy and its’ units of measurement.b. Use dot products to derive its value as a scalar. c. Solve equations for kinetic energy, mass or velocity

Benchmark # 2 Define and evaluate work. a. Derive equation for work and its’ units of measurement.b. Use dot products to derive its value as a scalar.c. Relate work to kinetic energy, and derive the equation for work as the change in kinetic energy.d. Solve equations for unknown values for force, displacement, work, kinetic energy, mass, velocity, or time.

Benchmark # 3 Evaluate work done by a variable force.a. Graph force vs. displacement for a varying force as it accelerates or slows down an object.b. Integrate this graph to find work, by calculating the “area under the curve.” c. Derive an equation for the curve of such a graph, and use calculus to integrate this equation for work done.d. Use this method to define and derive the work done by a spring or elastic force.e. Use integration to derive the equation for work done by a spring.f. Solve problems for unknown values, when a variable force is applied to an object.

1. Quizzes (2)- multiple choice on concepts in the chapter.2. Quizzes (2)-three problems each.3. Test-same format as the chapter test in part B.4. Homework-selected problems from the end of the chapter.5. Laboratory exercise-efficiency of an electric motor.6. Participation in Physics Olympics or Science Olympiad.7. Class participation for points.

1. Graphing calculator2. IBM PC3. PASCO 750 Interface Box4. PASCO smart pulleys5. PASCO force meters6. Vernier Graphical Analysis III Software7. Microsoft Excel & Word Software8. Electric power sources9. Electric motors10. Ammeters & voltmeters11. Wire connectors12. Ramps13. Pulleys14. Stopwatches15. Tabletop hardware

1. This is a critical unit in students’ development, because many of their previous problems can be solved using net force and kinematics OR conservation of energy. It is important to reinforce that either system may be used, and that they may use one system to check another.2. Topics that need to be spiraled are:a. Vector dot products, to find work and energy; vector cross products for the next unit to find angular momentum.b. Derivatives, and especially integrals, to find impulse caused by a variable force in the next unit.c. All units of measurement defined in terms of mass, length and time, in order to relate them to one another. These units are: force, work, energy, power, (and in the next unit), momentum, impulse and torque).d. Work and energy are scalars, even though you can get a value of negative work. In the next unit, momentum and impulse are vectors, and direction is one of the main differences between work/energy and momentum/impulse. Both systems may be used to solve certain problems.e. Eventually, this means certain problems may be solved with one of three systems: 1) net force/kinematics, 2) work/energy, 3) momentum/impulsef. Conservation is a concept unto itself. We use conservation of energy to solve closed systems. We introduce the conservation of matter and energy to explain nuclear fission and fusion. We will also use conservation of momentum in the next unit to explain how to solve




Benchmark # 4 Define and evaluate power.a. Derive both equations for power, and its’ units of measurement.b. Use dot products to derive its’ value as a scalar.c. Solve equations for unknown values of work, force, displacement, time, velocity, mass or kinetic energy.

Benchmark # 5 Define and relate “frames of reference” to motion and displacement.a. Derive equations to differentiate kinetic energy, work and power done in one frame of reference, compared to the other.b. Solve equations for all unknown values above as seen in one frame compared to the other.

Benchmark # 6 Define and evaluate potential energya. Derive an equation for potential energy and its’ units of measurement.b. Use dot products to derive its’ value as a scalar.c. Solve equations for potential energy, force or displacement.

Benchmark # 7 Define and relate conservative and non-conservative forces to potential energy.a. Derive equation for potential energy by conservative forces.b. Relate this equation to “path independence,” when solving for potential energy, (using conservative forces).c. Graph potential energy curve for any system of conservative forces.

problems with momentum. Then add the fact that when we include the conservation of kinetic energy, it differentiates between elastic and inelastic collisions.3. By now, students will have run at least one Physics Olympics tournament. Discuss the successes and failures, what worked well, what didn’t, strategies and tactics (like never lose any single event by a big score . . . you may not win an event, but never lose big). 4. This is about the “little past halfway point in the year.” This is a good time to assess students’ overall progress to date. They are seniors, and most will have their first semester sent to colleges they have applied to for admission. If you do not get on them right now, the second semester will see a real drop off in effort. Remind them that everything they learn this year, is something that you don’t have to relearn for next year. Their freshman year at college will be busy enough learning NEW material. Also, if you establish a brisk pace, you can ease up slightly, since the last two units on gravitation and equilibrium are quite straight- forward if you have been successfully spiraling topics all year. IT’S SECOND WIND TIME-GET ‘EM!




d. Use this graph to find potential and kinetic energy values.e. Use calculus or measured derivatives to find force on these graphs.f. Calculate the work done by non-conservative forces, especially friction.g. Solve problems for unknown values of potential or kinetic energy, force, mass, velocity, or displacement by any kind of force.

Benchmark # 8 Define and evaluate the conservation of Energy Principle.a. Derive a series of equations for any situation involving a closed system of an object (s) acted upon by a force.b. Solve problems for any closed system involving energy transfers.

Benchmark # 9 Define and relate matter and energy, in terms of conservation.a. Derive an equation for the energy found in matter.b. Define quantized energy, and relate it to phenomena in nature such as emission spectra, photo-electric effect, or photons measured in electron-volt units.


Essential Question, Concept or Theme: G. Momentum and Impulse Approx. Time Allotment:PA Standards: 3.1.12 A-E; 3.2.12 B-D; 3.4.12 A-C; 3.7.12 A-D


G.Benchmark # 1 Define center of mass, and relate it to a system of particles in three dimensions.a. Calculate the location of a center of mass in a system of particles, by finding its’ displacement, from a given reference, in one, two, or three dimensions. Use vector resolution.b. Calculate the velocity of a center of mass in a system of particles, in one, two, or three dimensions, using vector resolution.c. Calculate the acceleration of a center of mass in a system of particles, in one, two, or three dimensions, using vector resolution.d. Calculate the same acceleration of a center of mass, using the vector resolution of all the forces on all the particles in the system, (i.e.: the total net force of the SYSTEM).e. Equate this same system of particles to a single object, rotated or moved about its’ center of mass.

Benchmark # 2 Define and evaluate linear momentum.a. Derive an equation for momentum and its’ units of measurement.b. Identify and use this equation to produce a vector quantity.c. Calculate the linear momentum of a system of particles, using vector resolution of the total of all their momentum.

Benchmark # 3 Define conservation, and relate it to the concept of momentum before, during, and after a collision.

1. Two quizzes, both multiple choice will be given on concepts in the chapter.2. Two quizzes, with three problems.3. A test will be given with the same format as in the chapter test in part B.4. Homework will be selected problems from the end of the chapter.5. Laboratory exercise will be “Momentum in Two Dimensions.”6. Participation in Physics Olympics and Science Olympiad.7. Class participation for points.

1. Graphing calculator2. IBM PC3. PASCO 750 Interface Box 4. PASCO Smart Pulleys and Photogates5. PASCO Force meters and Accelerometers6. Air tracks, gliders, springs, magnets7. Vernier Graphical Analysis III Software8. Microsoft Excel and Word Software9. Two-dimensional Collision Devices10. Carbon Paper11. Meter sticks12. Stop watches13. Strobe lights and camera

1. This is one of the last “double chapter units” of the year. Watch your year-end scheduling. It students pick up on the concepts well, reduce the quizzing and MOVE ON! They have had much of this last year in Level I, so this is one area you can pick up time if you have suffered from class assemblies on lab days, pep rallies, early dismissals and senior cut days.2. Topics for spiraling in this unit are critical for the next unit (two chapters), in rotation and rolling. These topics are:a. Kinematics b. Vectorsc. Net Forced. Kinetic and Potential Energye. Work and Powerf. Momentum and Impulse

It is even worth a period or class session to do a quick overview or make a “key formula” list on the board . . . then when you are doing the next double chapter, show them that EVERY linear formula you have covered so far, has an EQUIVALENT rotational formula. Some have different units, some have the same units. There is also a key set of formulas that translate linear motion into rotational motion . . . highlight these.3. A warning should now be put up to begin three things:a. Preparing for the AP exam. As you spiral the main topics for a look at rotation, this is a good time to have students taking the AP exam do some extra problems . . . while you are stressing the CONCEPTS to the class.b. Become more demanding . . . “Up the




a. Derive an equation, based on momentum, for systems of particles, and identify their units of measurement.b. Solve problems for any system or type of collision, using momentum before and after an event, (i.e.: collision, explosion, applied force, joining together, etc.)

Benchmark # 4 Identify systems with a varying mass, and relate this to the “Conservation of Momentum Principle.”a. Derive an equation for a system of particles, SEPARATING from one another so that the mass of each unit changes, but the total system does not. (An example is a rocket ejecting its’ fuel out the back at tremendous speed, making the rocket’s mass lighter).b. Use integral calculus to derive an equation for the change in velocity of the unit or part of the system that you wish to measure. (Example: the rocket’s change in velocity).c. Evaluate the external forces and internal energy changes in a system of particles, and use the equations already derived, to find these values.d. Solve any problem, in a system of particles, for mass, displacement, time, velocity, acceleration, force or energy change, (gained or lost), using conservation of momentum.

Benchmark # 5 Define and evaluate Impulse.a. Define impulse as a collision and describe the interaction of systems of particles, center of mass, and forces involved.

ante.” Spend time critiquing lab reports. Go back and review the rubric; there aren’t many more labs left, and you want them to improve their report/analysis/writing/presentation skills. Also, take some of the best conclusions and copy them for everyone, “a good example.”c. Strategies and tactics: Every unit until now has been an extension of something learned last year. ‘Rotation’ and ‘Rolling,’ (two chapters), are the exceptions. An approach that can be taken at this point in the year is the “lecture format.” What is it like to go to college and have lectures? Can you really concentrate for an hour straight through? Take notes while someone is going that fast? What if you have a question, but you’re not allowed to raise your hand and ask? What is it like? How do you do it?I. Have them read the chapter on Rotation.II. Give them a full period lecture (no stopping, no questions from students permitted).III. Give them a quiz the next day (multiple choice, concepts)IV. Review the quiz the next day following, and discuss tactics on how to succeed under this kind of system: reading ahead, taking key notes ahead of time from the reading, listening more than writing, writing down main ideas only, etc.When this chapter is done, repeat I-IV for the chapter on ‘Rolling,’ to see if they can do it!




b. Derive both equations for impulse, involving force and time, and the change in momentum.c. Derive their units of measurement and mathematically compare them.d. Graph examples of a varying force on an object versus time, and find impulse, by finding the area under the curve, (integration).e. Use calculus, and with the formula for the curve, integrate this equation to find the impulse at any time.f. Solve problems and graphs for unknown values of impulse, momentum, force, time, mass, and velocity.

Benchmark # 6 Define and evaluate elastic and inelastic collisions, in one and two dimensions.a. Differentiate between elastic and inelastic collisions using the action of the objects after colliding, heat loss, and kinetic energy, before and after.b. Compare both elastic and inelastic collisions using the Conservation of Momentum Principle, and show they both conform to this law.c. Derive a series of equations for examples demonstrating collisions that are elastic, inelastic, and partially both.d. Solve these equations using vector resolution for conservation of momentum values, (i.e.: mass, velocity, direction).e. Solve these equations using kinetic energy conservation or loss to measure the percent elasticity during the collision.f. Solve problems involving “explosions” or decay, such as in radioactive atoms, with these same principles and energy loss.AP Physics C – Mechanics, Level I of 52 July 2002

Essential Question, Concept or Theme: H. Rotation and Rolling Approx. Time Allotment:PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.7.12.A, B, C, D, E; 3.8.12.A


Benchmark # 1 Define and differentiate between translation and rotation.a.) Define and derive units of measurement

for rotation.b.) Identify and define variables of rotationc.) Match and compare these variables of

rotation to their counterparts in linear translation.

d.) Match and compare both their units of measurement

e.) Identify which rotational variables are vectors, and which are scalars, using the right-hand rule.

Benchmark # 2 Define and evaluate rotation with constant acceleration.a.) Derive equations for rotational or

angular motion, and compare them to the kinematic equations for linear motion.

b.) Identify units of measurement for all variables

c.) Solve problems involving rotational or angular velocity, displacement, acceleration and time.

Benchmark # 3 Relate linear and angular variablesa.) Identify and differentiate between linear

and angular variables for velocity, displacement, acceleration and time.

1. Quizzes – 2 - multiple choice on concepts in chapter.2. Quizzes - 2 -three problems.3. Test - same format as the chapter test in part B.4. Homework - selected problems from the end of the chapter.5. Laboratory exercise – Conservation of angular momentum, OR, finding the Rotational Inertia of an unknown object. (Student lab groups may choose either one).6. Participation in Physics Olympics or Science Olympiad7. Class participation for points.

1. Graphing calculator2. IBM PC3. PASCO 750 Interface Box4. PASCO smart pulleys, photogates, laser switches 5. PASCO picket fences6. PASCO force meters7. Vernier Graphical Analysis III Software8. Microsoft Excel & Word Software9. Wood Ramps10. Discs, hoops, spheres, spools, etc, (made of wood, plastic, metal, etc.)11. Slotted weights and weight hangers12. Tabletop hardware13. Hinges, pivots, and connectors14. Meter sticks and rulers15. Stopwatches16. Electronic balance, (triple beam balance for larger objects).17. Sand and clay

1. If the strategies from the last unit, regarding lecture formats, were used and discussed by students . . . survey them now. Many like the approach, because the whole chapter is presented as a single unit. They see it front to back in one period. After that overview, it gives individual topics a “place” in the sequence. Extremely large sets of topics, like this unit, can be addressed to great advantage. The next three units, by contrast, are very short, and either approach is effective.2. TIME CHECK . . . how long until the AP Exam? This last unit, (all two chapters), is not covered at all in Level I Physics last year. Therefore, it deserves a thorough coverage. Of the next three units, EQUILIBRIUM is the easiest and most thoroughly covered to date. Do not do elasticity in the chapter, because it is not covered on the AP Exam. So do EQUILIBRIUM last, in case you need to hurry. The next chapter in the textbook is GRAVITATION. It is longer then EQUILIBRIUM, but fairly straight forward, and was covered last year.




b.) Derive equations translating angular motion into linear motion, (and vice versa), emphasizing proper units.

c.) Solve problems involving velocity, displacement, acceleration and time, in both angular and linear measurement, for objects which are rotating. Emphasize proper units, to reinforce which are linear and angular values.

Benchmark # 4 Define and evaluate rotational inertia.a.) Define and derive units of measurement

for rotational inertia.b.) Use calculus, (integral), to derive an

equation for rotational inertia.c.) Use this equation to find the rotational

inertia for several common objects, (i.e. hoop, disc, hollow and solid sphere, etc.), that rotate about their centers of mass.

d.) Use calculus to derive an equation to find the rotational inertia of these objects, when rotated around a point that is not at their center of mass.

e.) Use these equations to predict which objects will roll down a ramp faster or slower than other objects by proportionally comparing their rotational inertias. (Demonstrate this in class and lab).

f.) Solve problems for unknown values

Do it second to last. The next chapter is FLUIDS, ignore it; it is not on the AP Exam. Finally, OSCILLATIONS is the unit to do next after rotation/rolling. It is the least covered from last year, is longer, and students will be able to use their knowledge of angular velocity and its radian measure to calculate periodicity. Also, their calculators will still be in “radian mode,” along with their brains!

3. Topics to be spiraled:a. Units, units, units. First, these are ESSENTIAL in distinguishing between rotational values and linear values. Some must be emphasized, because they are the same, (units of work, energy, power, time, etc). You also encounter overlaps, such as BOTH torque and work have units of Nm, (Newtons x meters). So to distinguish them, we label energy units as joules. Finally units of radians are NOT units at all. They are a ratio of meters divided by meters, which equals one. So, if in a calculation, you obtain no units divided by time; that is actually angular velocity, measured in radians per second.




using formulas for rotational inertia in class, and in a laboratory exercise.

Benchmark # 5 Use Newton’s Second Law for rotation, to define and evaluate torque.a.) Define torque as an applied force

causing rotation, and identify the three factors which affect the size of its value. These are force; moment arm, (radius); and angle of applied force.

b.) Use these three values to derive an equation for torque, and derive its units of measurement.

c.) Differentiate these units of measurement from those of work and energy, using vector dot and cross products.

d.) Resolve these values vectorially, using cross products, to show that torque is a vector resultant; find its resultant direction using the right hand rule.

e.) Relate torque to Newton’s Second Law of Motion, and derive an equation for this law involving rotation of an object with mass.

f.) Derive units of measurement for this equation.

g.) Solve problems related to torque and the accelerated rotation of an object with mass, using Newton’s Second Law of Motion.

Benchmark # 6 Define and evaluate the

b. Derivatives and Integrals, especially as they relate to sine waves and sinusoidal functions. We will need this badly in the next unit. Also, we will need angular velocity again, to derive the equation for displacement of an oscillator. So emphasize the concept, and its units.c. The only oscillators they have not seen before, are a physical pendulum, and a torsional pendulum. Both rely upon finding the rotational inertia, I, of each object, and calculating the rotational Hooke’s Law constant, K. So, make sure you also emphasize rotational inertia; especially for a system of objects . . . AND UNITS of rotational inertia.d. Start making a formula page for the final exam-list; all formulas for linear and rotational equivalents NEXT TO EACH OTHER.4. By now, the Physics Olympics season is coming to an end, and the Science Olympiad season is beginning . . . make sure they end Olympics CLEANLY, (i.e., file all sample problems, event rules, maps, everything; put away all unused materials and label them; make lists of any information that




work, energy, and power of an object with mass, undergoing rotational motion.a.) Relate work, kinetic energy, and power

of an object in linear motion, to an object undergoing rotational motion.

b.) Derive an equation for work, kinetic energy, and power for a rotating object, and emphasize the units of measurement for each one.

c.) Relate the formula for kinetic energy of rotation, to rotational inertia, and compare the units of measurement for ALL values involved.

d.) Solve problems involving work, kinetic energy, power, and all related variables for an object or system undergoing rotation.

Benchmark # 7 Relate the major systems for rotation and their equations, so as to solve major problems using variables alone, or numerical values, when given. (This will involve algebra, trigonometry, calculus, and graphing, used in conjunction with one another).

Benchmark # 8 Define and evaluate rolling.a.) Differentiate rolling from rotation, and

define rolling as a specialized type of rotation.

b.) Vectorially describe the motion and velocity of ALL points on a rolling

came up and can be used again; display all awards in the library; notify the administration as to the year’s accomplishments, and update the banner in the library; put everything away and shut the machine down for the year!)5. Begin afternoon/evening extra help sessions: with practice multiple choice and free-form problems tests. Get them familiar with the test format; time restrictions; when to guess and when not to; problems with variables and no numbers; using written explanations for a problem, if you can’t do the math, (especially calculus); appropriate use of calculators; the experiment/graphing problem, etc… Basically, “Practice! Practice! Practice!”




object, as measured from a single reference point, (i.e. where the object touches the ground).

c.) Calculate the velocity and direction of ALL points, by vectorially adding the rotational and translational motions simultaneously.

d.) Derive the equations related to rolling, especially that for kinetic energy, and their units of measurement.

e.) Relate the translational velocity to the angular velocity, and derive their common value, (the radius of the object or wheel).

f.) Solve problems for any unknown value, related to an object rolling along, up, or down any inclined surface.

Benchmark # 9 Resolve rolling systems, or objects using systems of torque.a.) Use Free Body Diagrams, (F-B-D), to draw and label all forces on an object; translate them into torque vectors.b.) Use the concept of “moment arm,” to create systems of torques about ANY arbitrary or actual point of rotation.c.) Calculate the net torque on the system, including those created by friction or other contact forces.d.) Calculate the direction of rotation, and the rate at which it accelerates, for both rotation and translation.




e.) Solve problems for systems of torque, for any object or system of objects, rolling along a flat or inclined surface.

Benchmark # 10 Define and evaluate angular momentum for an object, or system of objectsa.) Define angular momentum and

differentiate it from linear momentum.b.) Derive the equation for angular

momentum, and its units of measurement.

c.) Using vector cross products, derive an equation for the angular momentum, created when an object with linear momentum strikes or collides with a system, which can rotate

d.) Define and derive the concept of Conservation of Angular Momentum, and the unique equation that is created for each example or system studied.

e.) Differentiate between systems which exhibit angular conservation of momentum and those that do not, based upon axes of rotation, slipping and friction, changes in rotational inertia, and systems of rotating objects.

f.) Find unique solution strategies and equations for systems which do NOT exhibit conservation of angular momentum.

g.) Solve problems, for selected variables,




involving single or systems of objects, which touch or connect, and transfer rotation to other objects or systems. Solutions may or may not be conservative, and if not, identify the losses of energy and/or momentum.


Essential Question, Concept or Theme: H. Rotation and Rolling Approx. Time Allotment: 4 weeksPA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.7.12.A, B, C, D, E; 3.8.12.A




Essential Question, Concept or Theme: I. Oscillations Approx. Time Allotment: PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.B, C; 3.6.12.C; 3.7.A, B, C, D, E; 3.8.12.C


Benchmark # 1 Define oscillation and periodic motion.

Benchmark # 2 Define and evaluate Simple-Harmonic-Motion (S-H-M)a.) Relate oscillation and periodicity

to S-H-M.b.) Relate displacement, velocity,

and acceleration (vectors) to S-H-M.

c.) Graph displacement, velocity and acceleration versus time for an oscillating object, (a sinusoidal curve).

d.) From these graphs, define and derive amplitude, period, frequency and wavelength for each one.

e.) Relate S-H-M to uniform circular motion in one dimension.

f.) Define this periodic motion in terms of angular velocity, ω, and derive its units of measurement.

g.) Derive the equation for displacement in terms of amplitude, angular velocity, time, and the sine of the angle they create, at any given moment in time.

h.) Compare this equation to the

1. Quiz - 1- multiple choice on concepts in chapter.2. Quiz - 1 - three problems3. Test - same format as chapter test in part B4. Homework - selected problems from the end of the chapter.5. Laboratory Exercise - Confirm the factors which affect a physical or torsional pendulum.6. Participation in Science Olympiad (Physics Olympics season has ended by now)7. Class participation for points.

1. Graphing calculator 2. IBM PC3. PASCO 750 Interface Box4. PASCO Smart pulleys, photogates, and laser switches5. PASCO picket fences6. PASCO force meters7. Vernier Graphical Analysis III Software8. Microsoft Excel and Word Software9. Physical springs and elastics of varying sizes10. Discs, hoops or spools, (made of plastic, wood or metal)11. Slotted weights and weight hangers12. Tabletop hardware13. Hinges, pivots, connectors14. Meter sticks and rulers15. Stop watches16. Electronic balance/triple beam balance17. Sand and clay

1. A reminder to leverage students’ knowledge of angular velocity, motion, acceleration, and displacement to develop the relationship between these variables and simple harmonic motion.2. This is the second major application of angular motion. Its resolution in formulas uses radian measure and its units of measurement. Practice a lot with units; make students use their calculators in radian, (not degrees) mode…over and over…again, until it is second nature. They see angular motion, they put their calculator into radian mode.3. This unit is the last major unit to utilize differential and integral calculus; to go back and forth between displacement equations and graphs, AND acceleration equations and graphs. Spending some extra time and emphasis here can help them review derivatives and anti-derivatives in general.4. Topics which need to be spiraled for the last two units:a.) Vector resolution is used here

for displacement, velocity, and acceleration. It will be used for




graph of displacement versus time, and demonstrate that they both represent the exact same motion…the displacement of the object at any moment in time.

i.) Using calculus, derive the equation for velocity with respect to time, from the displacement equation.

j.) Compare this equation to the graph of velocity versus time, and demonstrate that they both represent the exact same motion

k.) Using calculus, derive the equation for acceleration with respect to time, from the velocity equation.

l.) Compare this equation to the graph of acceleration versus time, and demonstrate that they both represent the exact same motion.

m.) Demonstrate from actual demonstrations and examples, that these graphs and equations may be used for ANY oscillating object in nature.

n.) Solve problems for any variable requested, using graphs or equations, for any oscillating object given.

FORCES in both of the last two units.

b.) Rotational inertia…by doing this unit right after rotational motion, it helps give more continuity in the lab, using the same basic ideas again, (especially rotational inertia and torque).

c.) Laboratory exercise-conclusions, and the rubrics used to grade them. By now, the level of their conclusions and how they are written should be quite high. Keep raising the bar!

d.) Review units for ALL variables by concentrating on the ones involved with your present unit…and differentiating them from others…make them identify these “other” units, and the variables they represent. Remember to STRESS linear variables and their units, AND rotational variables and their units.

e.) Continue building a single major formula page, for each student, to use as a year-end review for the final exam in this course; and to help




Benchmark # 3 Define and relate S-H-M to the varying force on an oscillating object.a.) Use Newton’s Second Law of

Motion to directly relate force and acceleration.

b.) Use the graph and equation of acceleration versus time to relate the net force on the object to the time.

c.) Use the graph and equation of displacement versus time to relate the net force on the object to its displacement.

d.) Use vector resolution to find the net force on an oscillating object, and its corresponding displacement, velocity, and acceleration at any moment in time.

Benchmark # 4 Relate specific oscillators to the general formulas and graphs derived for all objects in S-H-M.a.) Use Hooke’s Law to directly

relate force and displacement, when applied to a mass being acted upon by a spring or elastic.

b.) Through experimentation or demonstration, identify which factors affect an oscillator’s

organize all the formulas and their units into working relationships.

5. After school reviews, and evening help sessions; lunch clubs; and whenever you can give them practice problems and questions…go over them with the students!Practice, practice, practice…




period, (such as mass and spring constant affect the periodicity of an object being acted upon by a spring).

c.) Derive an equation, (using these unique factors), for each of the four specific kinds of oscillators:I. Simple PendulumII. Mass acted upon by a spring (elastic)III. Torsional PendulumIV. Physical Pendulum

d.) Solve problems for unknown variables using different kinds of physical oscillators.

e.) Confirm the factors and period equation, for one physical oscillator, in a laboratory exercise.

Benchmark # 5 Relate the overall Conservation of Energy Theorem, to an oscillator, by treating it as a closed system.a.) Define Potential Energy, (PE),

and Kinetic Energy, (KE), in an oscillator.

b.) Derive an equation for both PE and KE in an oscillator.

c.) Demonstrate and confirm that the total energy, E, in such a system is ALWAYS the sum of




KE plus PE.d.) Graph PE vs displacement for

any oscillator.e.) Use derivatives to find the force

at any point; the displacement to find the KE and PE at any point; and the constant total energy, E, at any point.

f.) Define and relate the work done by friction to, (heat), and the loss of kinetic energy in a non-closed system.

g.) Define and describe this loss as damping, and how it affects such variables as frequency, period, amplitude, energy, velocity, and acceleration.

h.) Derive an equation for damping.i.) Solve problems for unknown

variables involving energy, force, mass, displacement, velocity, acceleration, frequency, period, and amplitude at any position or time.


Essential Question, Concept or Theme: J. Gravitation Approx. Time Allotment: PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.6.12.C; 3.7.12.A, B, C, D; 3.8.12.A, B, C


Benchmark # 1 Demonstrate a working knowledge of the historical development of the theories of the universe, and solar system.

Benchmark # 2 Relate how these theories and developments affected the political/theological status of the past, (Renaissance), through to today.

Benchmark # 3 Define gravity as a force, with its units of measurement.

Benchmark # 4 Define gravitation as a field, and diagram this field about a mass located in space.

Benchmark # 5 Define and evaluate Newton’s Law of Gravitationa.) Derive Newton’s proportion for

gravitation.b.) Derive Newton’s equation for

gravitation, and define G, the universal constant for gravitation.

c.) Define the role of G in this equation, and derive its units of measurement.

1. Quiz – 1 - multiple choice on concepts in chapter.2. Quiz – 1 - three problems 3. Test - same format as chapter test in part B.4. Homework - selected problems from the end of the chapter.5. Laboratory exercise - “Circular Motion,” - derive and confirm the centripetal force with force meter or accelerometer.6. Participation in Science Olympiad.7. Class participation for points.

1. Graphing calculator2. IBM PC3. PASCO 750 Interface Box or remote 500 Interface Box4. PASCO force meters or accelerometers5. Vernier Graphical Analysis III Software6. Microsoft Excel and Word Software7. Brass weights (hanging and slotted)8. Tabletop Hardware9. Revolving stool or bicycle wheel10. String11. Pulleys12. Stopwatches

1. A key point in this unit, and the cause of a major misconception is the DIFFERENCE between gravitational Potential Energy, (PE), when it is near the Earth’s surface, or when it is far away. Near the surface, it is:

PE= mgh

where ‘h’ is the height above the surface. Far out in space the formula is:______________________________________________________________________________PE= Gm1m2 __________

R

where R is the distance between the CENTER of m1, and the CENTER of m2. The surface distance is ignored. The real difference between the two is in problem solving. The first formula basically ignores the change in g, the acceleration due to gravity, because it remains so close to the surface. It is concerned with problems done on our planet’s




d.) Relate how Cavendish’s experiment measured the value of G.

e.) Solve problems for unknown values using Newton’s gravitation equation.

Benchmark # 6 Define and evaluate the Principle of Superposition.a.) Use vector resolution to find

gravitational forces in space; near the earth’s surface; and inside the Earth.

b.) Use vector resolution to find gravitational forces and field lines, between multiple (major) masses in space.

c.) Solve problems for unknown values using Newton’s gravitation equation and vector resolution.

Benchmark # 7 Define and evaluate gravitational potential energy.a.) Derive an equation for the

gravitational potential energy of an object in space, (above the earth’s surfacing); use the concept of the work done, to place it there from the earth’s

surface, (usually by people). Therefore, as a rule of thumb, tell students that when doing problems, which remain in the Earth’s atmosphere, use the first formula. When doing problems, which involve Earth satellites or problems in “outer space,” use the second formula. This difference MUST be addressed, however.

2. Topics that are finished being spiraled here are: a.) Conservation of energy-this

topic is necessary when deriving the formula for escape velocity and satellite orbits. MAKE SURE, you address the rotational and linear velocity of the Earth launch site, and the kinetic energy a rocket has EVEN WHEN SITTING ON THE LAUNCH PAD. It is why Cape Kennedy is located as far SOUTH as possible in the United States. Also, why rockets are directed eastward after launch, to utilize this kinetic energy that it already has, and increase it.

b.) To do most gravitation problems, six formulas are




surface.b.) Derive the units of

measurement for this gravitational Potential Energy, (PE).

c.) Differentiate between gravitational PE near the earth’s surface, and much further out in space.

d.) Differentiate between the equations used to find these two values, and explain the discrepancy between the distances from the Earth’s center, (when calculating these values).

e.) Relate gravitational PE to Kinetic Energy, (KE), of objects moving in relation to Earth.

f.) Use this relationship to derive the equation for Escape Velocity from the Earth’s gravitational field.

g.) Use the formula for escape velocity, to relate how orbits combine gravitational PE and KE in the conservation of energy principle.

h.) Solve problems for unknown variables using the principles of gravitational PE and the overall

necessary, and it is critical to show how they relate to one another. They are the formulas for: I. Newton’s Law of GravitationII. Kepler’s Third Law of Planetary MotionIII. Velocity of an object in circular motionIV. Centripetal ForceV. Escape VelocityVI. Conservation of mechanical energy, (PE and KE)

c.) One common “trick question” that is used by many teachers to see if students truly understand these relationships, is that of a “twin star” situation. The key is that the radius of their orbits, R1, is used in the centripetal force equation; the distance between their centers, R2, is used in the gravitation formula. Therefore, R2 is twice as big as R1. This is one of the very few exceptions that occurs -where R1 does NOT equal R2.

3. Finally, this unit has been




conservation of energy.

Benchmark # 8 Define and evaluate Kepler’s Laws of Planetary Motiona.) Define and draw an ellipse.b.) Identify its major

characteristics, (major/minor axes, foci, center, etc.)

c.) Define and derive the equation for eccentricity in ellipses.

d.) Relate this definition to Kepler’s First Law, and how all orbiting objects in space follow this principle.

e.) Identify the position of masses orbiting and being orbited; maximums and minimums; the acceleration and velocity of the orbiting satellite; and how this affects the center of mass while orbits occur.

f.) Relate the area swept out during orbit, to the equal intervals of time that create these areas, in Kepler’s Second Law of Planetary Motion.

g.) Define and derive the equation for Kepler’s constant, in his Third Law of Planetary Motion.

h.) Relate which bodies use the same constant, and differentiate

dogged with student complaints in the past, which basically asked, “How does this relate to everyday…?” Tell them: In today’s marketplace, (full of satellite TVs, cell phones, pagers, etc.), there is a tremendous growing need for more communications satellites, that go beyond spy satellites and weather satellites put up by NASA. Several companies in the U.S. and abroad, now regularly launch their own satellites for private industry. These companies need, for technical people, will only increase in the future. NASA is no longer the only way into space.

4. One last “Gee, wow!” look, at the universe. It is relevant here, and is a small look at gravity waves and why they exist. Also, how they relate to the “Big Bang” theory of the birth of our universe, and how we would use them to discover the age of our universe…all care of gravitation!




which bodies use different constants, for all objects in space.

i.) Solve problems for unknown variables using Kepler’s Laws of Planetary Motion.

Benchmark # 9 Solve for unknown variables, by relating Newton’s Law of gravitation, with equations for: acceleration, centripetal force, kinetic and potential energy, mass, circular motion, and Kepler’s Third Law.

Benchmark # 10 Define and relate Einstein’s theory of gravitation with three-dimensional space.a.) Define the relationship

(according to Einstein) between mass and gravity.

b.) Relate this to the “distortion” of space around a large mass, then a smaller mass.

c.) Use this “model” of “bent space” to explain all the possible motions of moving objects, coming near a large mass in space.

d.) Use this model to explain how a black hole can be created in “bent space.”




e.) Explain how black holes can be detected and mapped in the universe.


Essential Question, Concept or Theme: J. Gravitation Approx. Time Allotment: 4 weeksPA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.6.12.C; 3.7.12.A, B, C, D; 3.8.12.A, B, C




Essential Question, Concept or Theme: K. Equilibrium Approx. Time Allotment: 4 weeksPA Standards: 3.1.12.A, B, C, D; 3.2.12.A, B, D; 3.4.12.C; 3.6.12.C; 3.7.12.A, B, C, D, E


Benchmark # 1 Define and evaluate equilibrium, at a single point.a.) Derive an equation for

equilibrium as the sum of all force vectors equals zero.

b.) Relate these forces as all coming from a single point.

c.) Resolve all force vectors into components.

d.) Redefine equilibrium as force components:I. The sum of all force components on the x-axis equal zero.II. The sum of all force components on the y-axis equal zero.III. The sum of all force components on the z-axis equal zero.

e.) Define the center of gravity as representing: all gravity, on all parts of an object.

f.) Solve problems for unknown variables involving the vector resolution of all forces on an object.

Benchmark # 2 Define and evaluate equilibrium, when forces are applied to different points on an

1. Quiz – 1 - multiple choice on concepts in chapter2. Quiz - 1 - three problems3. Test - same format as chapter test in part B4. Homework - selected problems from the end of the chapter5. Laboratory exercise - student originated and designed, from any topic throughout the year.6. Participation in Science Olympiad7. Class participation for points

1. Graphing calculator2. IBM PC3. PASCO 750 Interface Box4. PASCO Smart pulleys, photogates, and laser switches5. PASCO force meters, accelerometers, picket fences6. Vernier Graphical Analysis III Software8. Microsoft Excel and Word Software9. Tabletop hardware10. Any other resources previously mentioned, or materials necessary for students to build their own devices and test platforms.

1. All the separate concepts for this unit have been seen before. They merely must be brought together, in a formal presentation, with the EMPHASIS ON EXAMPLES. Also, concentrate on systems where BOTH force vectors AND torque are needed to solve these problems. Be sure to include friction, as a means to review; constantly require both components and resultant forces at a single point. This is strong review material. Remember, both the AP Exam and the course final exam are coming VERY SHORTLY.2. The course final exam is a former AP Exam, given some years back. A new group of multiple choice questions AND free form problems, are selected each year from the collection of past AP Exams, (sent to the teacher, after their formal training by the College Board instructors). The course final exam is traditionally given a few days after the AP Exam: 35 multiple choice questions during one class period; 3 free-form problems, (selected by students from 5 possible), during another period. These may be over two days or a double lab period…THE




object.a.) Redefine torque as a force;

applied to a moment arm; at some distance from a pivot point; at an angle to that moment arm.

b.) Select any arbitrary pivot -point, and identify all the torques applied to the object using one or more moment arms.

c.) Vectorially resolve all torques involved in equilibrium, by labeling them clockwise or counter -clockwise around this pivot point.

d.) Derive torque equations for equilibrium as the sum of all clockwise torques plus the sum of all counter –clockwise torques equal zero.

e.) Calculate the sum of all force components is also equal to zero, when no rotation is involved.

f.) Solve problems for unknown variables involving the vector resolution of both force components, and torques applied to an object.

Benchmark # 3 Relate the

INCENTIVE is, study ONCE, and take the AP Exam AND the course final exam within a few days of each other. This will hopefully encourage students to sign up for the AP Exam.3. Needless to say…PRACTICE, practice, practice!!!4. The final exam and AP Exam now out of the way, their year now has about two weeks until classes are over, and regular final exams begin. This is when AP Physics does their final formal lab project: a lab of their own choice, and their own design - any topic you have covered. They may choose their own lab partners, (up to six, maximum), and it can be a new topic, or an extension of something they have done before. It can even be related to Science Olympiad or Physics Olympics. BUT it is a formal laboratory exercise, turned in by the start of regular final exams, and graded as a major chapter test. When done properly, this is a fun time to really see some creative thinking, building, and evaluating! For the most part, the pressure is off, and this is CREATIVE TIME, for MOST are seniors.




motion of an object to equilibrium.a.) Demonstrate that objects at

rest, or constant velocity in a straight line, are in equilibrium.

b.) Demonstrate that objects not rotating, or rotating at constant angular velocity, are also in equilibrium; their net torque equals zero.

c.) Demonstrate that systems of objects, exhibiting these characteristics are also in equilibrium.

d.) Solve problems for unknown variables, involving single objects or systems of objects, moving as described above.

5. One last very important step…stay in touch with these students after they graduate. Have them bring back syllabi and lab manuals from the colleges and universities they are attending. Have them critique this course for strong and weak points; level of difficulty; appropriate topics; time dedicated to each topic; lecture and class time usage; laboratory exercises and lab write-ups; and all the ideas they bring up to make this course stronger EVERY year. This particular course has evolved for 22 years, and has NEVER been taught the same twice in a row. USE all the research tools available to you: Physics Teacher Magazine and other publications; the American Association of Physics Teachers, (the AAPT), and National Science Teachers Association, (the NSTA), and other organizations; competitions like Physics Olympics and Science Olympiad, and their coaches and activities; the numerous web sites for teachers and students to use; new textbook offerings, which will be sent to you on request from publishers, (also ask for the teacher’s edition and other




accompanying manuals); and visitations to other schools, especially events like Middle States Evaluations; ETC…Remember - in a topic area like physics, if you are not constantly trying to improve and update…you are not standing still - you are losing ground!!


Essential Question, Concept or Theme: K. Equilibrium Approx. Time Allotment: PA Standards: 3.1.12.A, B, C, D; 3.2.12.A, B, D; 3.4.12.C; 3.6.12.C; 3.7.12.A, B, C, D, E




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